9-1 Quadratic Graphs and Their Properties Graph y = ax2 + c

Vocabulary A quadratic function is a nonlinear (not a line) function that can be written in the standard form y = ax2+ bx + c where a ≠ 0 Every quadratic function has a U-shaped graph called a parabola.

Vocabulary The most basic quadratic function in the family of quadratic functions, called the parent quadratic function, is y = x2 X -2 -1 1 2 Y = 4

Parts of a Parabola The lowest or highest point on a parabola is the vertex. The line that passes through the vertex and divides the parabola into two symmetric parts is called the axis of symmetry.

How does the coefficient a effect the graph? Graph y = ax2 How does the coefficient a effect the graph? If “a” is positive (a > 0) then the graph opens up. If “a” is negative (a < 0) then the graph flips upside down or it opens down. (Or as I like to call it…makes a SAD face)

Graph y = ax2 How does the coefficient a effect the graph? a can stretch or compress the parabola. If |a| > 1, then graph is stretched. (i.e. y = 2x2, y = -3.5x2 , ) If |a| < 1, then the graph is compressed. ( i.e. , , )

Example 1: Graph y = 2x2. Compare the graph with the parent function, y = x2. You need to make a table of values. X -2 -1 1 2 Y =

You Try: Graph y = 1/2x2. Compare the graph with the parent function, y = x2. X -2 -1 1 2 Y =

Example 2: Graph y = -3x2. Compare the graph with the parent function, y = x2. You need to make a table of values. X -2 -1 1 2 Y =

Graph y = ax2 + c The constant “c” moves the graph up or down. If “c” is positive (c > 0) it moves the graph up. if “c” is negative (c < 0) it moves the graph down.

Example 4: Graph y = x2 + 2. Compare the graph with the parent function, y = x2. You need to make a table of values. X -2 -1 1 2 Y =

You Try: Graph y = x2 – 4. Compare the graph with the parent function, y = x2.

Homework: Book: 9.1 p.550 #13-22, 33-36, 47, 58-63